Kenyan forces have secured an upscale Nairobi shopping mall, killing three suspected terrorists and promising to "punish" any others they encounter, following a three-day hostage standoff with an al Qaeda-linked rebel group that has killed at least 62 people and injured 175, police said.

"We have taken control of all the floors," Kenyan police said via an official Twitter account. "We're not here to feed the attackers with pastries but to finish and punish.

"We can confirm that three terrorists have been killed so far, a few others have suffered injuries."

Another 11 suspects were arrested and are undergoing questioning, police said.

Large plumes of black smoke were seen rising over the building and volleys of automatic gunfire could be heard, as soldiers stormed the mall this afternoon local time.

Officials believe most of the hostages were removed from the building as forces went floor to floor searching for suspected terrorists associated with al-Shabab, an Islamist terror organization based in Somalia.

"[Kenya Defense Forces] has dominated all floors of Westgate Mall building. Troops are now concentrating on clearing the building," police tweeted.

Eleven soldiers were injured in the attack and are being treated for injuries, according to authorities.

Sporadic gunfire was heard throughout the early morning hours after officials pledged late Sunday night that they would end the deadly siege overnight in hopes of freeing the last remaining hostages. Authorities claimed to have cleared much of the Westgate Mall and rescued most of the hostages who had been held since Saturday.

The official death toll rose overnight to 62, according to the Kenyan Red Cross, but the number could rise as more parts of the building are cleared.

"We urge Kenyans to keep away from West Gate as the security agencies do all that must be done to end the siege ASAP," Kenyan police tweeted today.

Kenyan authorities had said they would do their utmost to save hostages' lives, but no officials could say precisely how many people were being held captive.

"We urge all Kenyans to be patient. We are frayed & tired, but No, this is not the time to give up. All agencies are doing what must be done," Kenya's Ministry of Interior tweeted earlier today.

He said security forces had rescued more than 1,000, Kenya President Uhuru Kenyatta said Sunday night.

Kenya's National Disaster Operation Centre late Sunday tweeted that "this will end tonight. Our forces will prevail."

The military assault began shortly before sundown Sunday, with one helicopter skimming very close to the roof of the shopping complex as a loud explosion rang out, far larger than any previous grenade blast or gunfire.

Kenyan police said on Twitter that security forces had launched a "MAJOR assault" assault to end the bloody siege.

Col. Cyrus Oguna, a Kenyan military spokesman, said late Sunday that many of the rescued hostages, mostly adults, were suffering from dehydration. He said some of the attackers had "most probably" been killed in the operation.

Police had been largely tight-lipped since their assault began Sunday night, fearing that the terrorists inside were monitoring media reports.

Somalia's al Qaeda-linked rebel group, al-Shabab, claimed responsibility for the attack, saying that it was in retaliation for the 2011 involvement of Kenyan forces in their country to fight the Islamic insurgents.

Rep. Peter King told "This Week" the attack was "very sophisticated" and shows the ongoing ability of al Qaeda and its affiliates to inflict terror.

"It's an extremely deadly organization, very well trained. And it's one of the only al Qaeda affiliates which actually has actively recruited here in the United States," King, R-N.Y., said.

Five Americans are among the wounded, State Department Deputy Spokeswoman Marie Harf said in a statement.
There were no reports of any U.S. casualties, Harf said.

But the Australian, British, Canadian, French, Ghanaian and Somali governments have acknowledged the deaths of their citizens, along with Kenyan nationals killed in the "despicable massacre of innocent men, women and children," she said.

British Prime Minister David Cameron is cutting short his annual weekend with the Queen at Balmoral Castle in Scotland to return to London to chair a meeting of the U.K. government's emergency committee dealing with the attacks in Kenya.

Before leaving for Balmoral, Cameron warned the British people they should be braced for "more bad news" from Nairobi.

The Westgate Mall is a destination for Kenya's elite. It bills itself as the city's premiere mall, boasting that it offers customers a "first world interior" and a "safe and serene environment."

It opened in 2007 and has more than 80 stores.

ABC News' Alexis Shaw and The Associated Press contributed to this report.